Been there, done that. Heres how:
Forget taping anything, tape and backglass seldom play nice.
Cut squares out of poster board the same size as the areas that need to remain clear.
Take Q-tips and windex and clean the "windows",
Spray the cut pieces of posterboard with a LOW tack spray adhesive and let them sit for a minute or two.
Take a hobby size exacto knife and stick one of the pieces of posterboard to it and use the exacto to line it up to the window. Then press down on the posterboard, keep your finger on it and twist the exacto until it comes off and press the piece in place. If you dont like the placement use the exacto to lift it and re align it. Scraped some of the white in the process? Who cares you're painting it over anyway.
Once all the window pieces are in place cut another piece of posterboard with a whole big enough to mask off the white area. DO NOT SPRAY WITH ADHESIVE. This piece can be held down with a few quarters, overspray is no big deal because the area flush to the white is silvered out and shows no light. Cut a few more larger pieces of posterboard to cover the general area as a whole but just lay them in place.
The paint to use is Bullseye spray primer in a rattle can. Shake it...alot. test it on a scrap piece of posterboard and when your comfortable with how it acts. Lay a quick coat, do not look to cover in one coat. Check all your masked areas if everything acted as it should spray another coat or two until covered.
Once dry carefully use the exacto to remove the pieces covering the windows, any residual spray adhesive can either be scraped with a razor or wiped with a q-tip and denatured alcohol. If using the denatured alcohol wring the q-tip out as it WILL remove your fresh white paint.